I think the verb is really "mitfeiern", and the other two mits are just additional information. Maybe it's because I'm from the North, to me the double mit doesn't sound awkward. Of course, the solution @0x6d64 provided is a nice alternative.
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OregonGhostJul 25 '12 at 9:38

To make an amendment to Em1's answer: There is a small difference between

Bring deinen Schlafsack.

and

Bring deinen Schlafsack mit.

In the second sentence someone is asked to bring along the sleeping bag, the first sentence sounds like you want the other person to bring the sleeping bag over, and then leave. However, if we talk about an invitation everybody understands that they are welcomed to stay and not just "bring the sleeping bag": In every other case the other person would state explicitly some kind if request:

Bring deinen Schlafsack, even in the mentioned context, still sounds incomplete (actually: denglisch) to me. You would include some word, like Bring deinen Schlafsack vorbei or Bring mir deinen Schlafsack.
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MrmfldmnNov 30 '12 at 11:09

I think this qualifies as "social skills of a thermonuclear device", especially the first paragraph, unless you're trying to be sarcastic, but then it's simply not funny. Did you ever meet someone who would write an invitation like that and actually mean what you suggested? I agree that there may be better alternatives, like the one 0x6d64 suggested, but that doesn't make the original sentence having such a mean meaning. Never attribute to malice what may just be colloquial usage.
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OregonGhostJul 25 '12 at 9:46